[R] Issues when trying to fit a nonlinear regression model

[Bert Gunter]

I got starting values as follows:
Noting that the minimum data value is .38, I fit the linear model log(y -
.37) ~ x to get intercept = -1.8 and slope = -.055. So I used .37,
exp(-1.8)  and -.055 as the starting values for theta0, theta1, and theta2
in the nonlinear model. This converged without problems.

Cheers,
Bert


On Sun, Aug 20, 2023 at 10:15 AM Paul Bernal <paulbernal07 using gmail.com> wrote:

> Dear friends,
>
> This is the dataset I am currently working with:
> >dput(mod14data2_random)
> structure(list(index = c(14L, 27L, 37L, 33L, 34L, 16L, 7L, 1L,
> 39L, 36L, 40L, 19L, 28L, 38L, 32L), y = c(0.44, 0.4, 0.4, 0.4,
> 0.4, 0.43, 0.46, 0.49, 0.41, 0.41, 0.38, 0.42, 0.41, 0.4, 0.4
> ), x = c(16, 24, 32, 30, 30, 16, 12, 8, 36, 32, 36, 20, 26, 34,
> 28)), row.names = c(NA, -15L), class = "data.frame")
>
> I did the following to try to fit a nonlinear regression model:
>
> #First, Procedure to Find Starting (initial) Values For Theta1, Theta2, and
> Theta3
>
> mymod2 <- y ~ theta1 - theta2*exp(-theta3*x)
>
> strt2 <- c(theta1 = 1, theta2 = 2, theta3 = 3)
>
> trysol2<-nlxb(formula=mymod2, data=mod14data2_random, start=strt2,
> trace=TRUE)
> trysol2
> trysol2$coefficients[[3]]
>
> #Fitting nonlinear Regression Model Using Starting Values From Previous
> Part
> nonlinearmod2 <- nls(mymod2, start = list(theta1 =
> trysol2$coefficients[[1]],
>                      theta2 = trysol2$coefficients[[2]],
>                      theta3 = trysol2$coefficients[[3]]), data =
> mod14data2_random)
>
> And I got this error:
> Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff, nDcentral =
> nDcntr) :
>   singular gradient matrix at initial parameter estimates
>
> Any idea on how to proceed in this situation? What could I do?
>
> Kind regards,
> Paul
>
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>
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